@vax, everywhere you have listed is stinger affected at that time. But, depends what you want to do, if you want to go snorkeling, see reef areas etc, then you just wear a stinger suit. They are really lightweight and cover hands but you can still use them (being your hands). Any company that you use to go out snorkeling/exploring should provide them included in the cost at that time of year.
If you are interested in that area, maybe some of the nicer areas around Port Douglas. Make sure you do Karunda, takes a day and do the rainforest sky car up and steam train back down, not the other way. Would also do Hartley’s crocodiles, and lots of trips out to the reef platforms or islands. Personally, I’d do a reef/island trip out every second day based somewhere like Douglas rather than staying somewhere like Hamilton. If you were not have a car (??) I think most reef companies will pick up from major hotels, but check that. I always have a car in those areas but pretty sure I’ve seen people bused in to reef transfer shops. Look at someone like Quicksilver. Make sure you make a day for Daintree proper as well, never ceases to amaze me.
I’m actually based in Sydney but do the reef and Daintree area every second/third year.
Have you looked at Kakadu/Katherine Gorge? If I were you, I’d look at splitting the time. Pretty sure there are flights over to Darwin from Cairns or Townsville. Then do a tour encompassing Kakadu and Katherine, back up through Litchfield. I wouldn’t hire a car though if you are not used to outback driving. Seriously, one night in Darwin either side of tour is more than enough as the only reason to be there is a sunset. A lot of people like Mindil beach for that purpose but I’d recommend a sunset cruise - do a fish and chip one not the expensive 3 course ones as the sunset doesn’t change🤣.